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Title: Mandelbrot and Julia Sets via Jungck-CR Iteration with s-convexity
Authors: Kwun, Young Chel
Tanveer, Muhammad
Nazeer, Waqas
Gdawiec, Krzysztof
Kang, Shin Min
Keywords: Julia set; Jungck-CR iteration; Mandelbrot set; s-convex combination
Issue Date: 2019
Citation: IEEE Access, Vol. 7 (2019), s. 12167-12176
Abstract: In today’s world, fractals play an important role in many fields, e.g., image compression or encryption, biology, physics, and so on. One of the earliest studied fractal types was the Mandelbrot and Julia sets. These fractals have been generalized in many different ways. One of such generalizations is the use of various iteration processes from the fixed point theory. In this paper, we study the use of Jungck-CR iteration process, extended further by the use of s-convex combination. The Jungck-CR iteration process with s-convexity is an implicit three-step feedback iteration process. We prove new escape criteria for the generation of Mandelbrot and Julia sets through the proposed iteration process. Moreover, we present some graphical examples obtained by the use of escape time algorithm and the derived criteria.
DOI: 10.1109/ACCESS.2019.2892013
ISSN: 2169-3536
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